The aim of the present book is a uni?ed representation of some recent results in geometric function theory together with a consideration of their historical sources. These results are concerned with functions f, holomorphic or meromorphic in a domain ? in the extended complex planeC. The only additional condition we impose on these functions is the condition that the range f(?) is contained in a given domain C.Thisfactwillbedenotedby f? A(?, ?). We shall describe (n) how one may get estimates for the derivatives-f (z )-, n?N, f ? A(?, ?), 0 dependent on the position of z in ? and f(z)in?. 0 0...